# Learning with Partially Ordered Representations

## TL;DR

This paper introduces a novel approach to grammar learning using partially ordered string representations, enabling more flexible modeling of shared properties at string positions and improving learning efficiency.

## Contribution

It presents a new model-theoretic framework for grammars with shared, multi-property positions and an algorithm that efficiently learns the most general grammar from positive examples.

## Key findings

- Structures are shown to be partially ordered.
- The learning algorithm effectively prunes the hypothesis space.
- It finds the most general grammar covering the data.

## Abstract

This paper examines the characterization and learning of grammars defined with enriched representational models. Model-theoretic approaches to formal language theory traditionally assume that each position in a string belongs to exactly one unary relation. We consider unconventional string models where positions can have multiple, shared properties, which are arguably useful in many applications. We show the structures given by these models are partially ordered, and present a learning algorithm that exploits this ordering relation to effectively prune the hypothesis space. We prove this learning algorithm, which takes positive examples as input, finds the most general grammar which covers the data.